The number 54720
54720 is a composite number with 84 divisors. Its prime factorisation is × × 5 × 19. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24 … 54720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 54720: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
54720 is composite. Its prime factorisation is
- 3
The divisors add up to 198120; without 54720 itself that is 143400, so 54720 is abundant (143400 is more than 54720). Euler's totient φ(54720) = 13824 numbers up to 54720 share no factor with it.
- 4
The digits of 54720 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54720 = 2^{6} \times 3^{2} \times 5 \times 19 \]54720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 198120 |
| Euler totient φ(n) | 13824 |
| Square | 2994278400 |
| Cube | 163846914048000 |
| Square root | 233.923064 (= 24√95) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 60 |
| Scientific notation | 5.472 × |
54720 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand seven hundred and twenty |
| Binary (base 2) | 1101010111000000 |
| Octal (base 8) | 152700 |
| Hexadecimal (base 16) | D5C0 |
| Base 3 | 2210001200 |
| As time | 54720 seconds = 15 h 12 min 0 s |
Is 54720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54720 ÷ 2 = 27360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54720 ÷ 3 = 18240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54720 ÷ 4 = 13680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (54720 ÷ 5 = 10944) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54720 ÷ 6 = 9120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (54720 ÷ 8 = 6840) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (54720 ÷ 9 = 6080) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (54720 ÷ 10 = 5472) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (54720 ÷ 12 = 4560) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54720 a prime number?
No. 54720 = × × 5 × 19, so it is divisible by 2.
What are the factors of 54720?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 32, 36, 38, 40, 45, 48, 57, 60, 64, 72, 76, 80, 90, 95, 96, 114, 120, 144, 152, 160, 171, 180, 190, 192, 228, 240, 285, 288, 304, 320, 342, 360, 380, 456, 480, 570, 576, 608, 684, 720, 760, 855, 912, 960, 1140, 1216, 1368, 1440, 1520, 1710, 1824, 2280, 2736, 2880, 3040, 3420, 3648, 4560, 5472, 6080, 6840, 9120, 10944, 13680, 18240, 27360, 54720.
What is 54720 in binary?
1101010111000000 (hexadecimal D5C0, octal 152700).
What is the square root of 54720?
About 233.9231, exactly 24√95.
Is 54720 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 54720?
54720 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.